Question: Simplify the following expression: $ k = \dfrac{1}{7} + \dfrac{5r - 5}{r + 2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r + 2}{r + 2}$ $ \dfrac{1}{7} \times \dfrac{r + 2}{r + 2} = \dfrac{r + 2}{7r + 14} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{5r - 5}{r + 2} \times \dfrac{7}{7} = \dfrac{35r - 35}{7r + 14} $ Therefore $ k = \dfrac{r + 2}{7r + 14} + \dfrac{35r - 35}{7r + 14} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{r + 2 + 35r - 35}{7r + 14} $ $k = \dfrac{36r - 33}{7r + 14}$